The ability to absorb, adapt, and recover from disruptions -- also termed resilience -- is a beneficial characteristic of any natural or anthropogenic system, including energy systems, that are exposed to natural hazards. Energy systems that supply us with fuel and electricity are essential for the health and prosperity of most communities around the world. Increasing the resilience of these systems and, thereby, minimizing disruption in critical services, such as telecommunications and water treatment, is an often stated goal of policy makers, regulators, and utilities. This goal, however, has proven difficult to achieve due to a lack of standardized resilience practices. The research presented in this dissertation develops a measurement framework that can inform the development of analytical models and develops two analytical models that examine the resilience of electric power systems using empirical data. Broadly, the research presented in this dissertation contributes to the fields of disaster management and energy systems in relation to vulnerability, risk, and resilience by examining theoretical perspectives and testing analytical methodologies with empirical power outage data. The findings of this dissertation will hopefully facilitate the development of energy system planning and management approaches that incorporate resilience as a key principle rather than regulatory jargon.